In this paper we present the theoretical foundation of forward error analysis of numerical algorithms under;• Approximations in "built-in" functions.• Rounding errors in arithmetic floating-point operations.• Perturbations of data.The error analysis is based on linearization method. The fundamental tools of the forward error analysis are system of linear absolute and relative a prior and a posteriori error equations and associated condition numbers constituting optimal of possible cumulative round – off errors. The condition numbers enable simple general, quantitative bounds definitions of numerical stability. The theoretical results have been applied a Gaussian elimination, and have proved to be very effective means of both a prior

The term "semantic exchange" was popularized in Arabic, especially in derivatives, grammatical structures, etc., but it came under different names or terms, including deviation, deviation, transition, displacement, tooth breach, replacement, attention, etc. In the rooting of this term through its study in language and terminology, and among linguists, grammar and others, we have reached a number of results, including The existence of a harmonization between the lexical and idiomatic meaning of the term exchange, and the phenomenon of semantic exchange is a form of expansion in language, and that the first language scientists They had turned to this And studied under Cairo for different names, as noted above.

The idea of this research is based on presenting a study specialized with the rules and bases of the Iraqi methodological music composition of the Symphony Orchestra according to the construction of the musical compositions of great forms and which are characterized by the melody difference and variation within their musical fabric according to the method of distributing the instruments and their types within the orchestra. The researcher has been interested in studying this building based on what is written for him according to the stringed instruments arc instruments and bass, which is represented by the cello and the contrabass. It is possible through the analysis of the melody structure features of these instruments and the melody re

This study investigates the impact of agricultural investment policy—represented by agricultural loans and investment allocations—on rice crop production in Iraq over the period 2003–2023, employing the Autoregressive Distributed Lag (ARDL) model. Using time-series econometric analysis, the study confirms a short-term positive and statistically significant effect of financial support on rice output, while revealing statistically insignificant long-term effects. The presence of a cointegration relationship suggests long-term equilibrium between agricultural policy variables and rice production. However, the absence of causality in the Yamamoto-Toda test implies that structural and institutional inefficiencies may dilute the long-term i

The interest in the issue of capital movement as an economic phenomenon has increased because of its effects and effects and its ability to influence the economic balance and the effectiveness of monetary policy. All countries seek to attract capital and benefit from it because of its effects and results such as supporting economic development process and optimal allocation of economic resources. The problem of the financing gap that most countries suffer from, and others, but sometimes the movement of capital creates challenges for monetary policy makers in achieving their goals.

   After 2003, the Iraqi economy witnessed an openness and economic liberalization unlike previous years, which